F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

Johansen's stepped yield criterion 295
unit width. Where two moment axes are shown for a slab, it means that
there are two bands of reinforcement. Thus, in Fig. 8.3-l(c) and (d), the
presence of both m 1 and m 2 moment axes shows that there is a band of
reinforcement m 1 normal to the m1 axis, and another band m2 normal to
the m 2 axis. Note in particular that m 1 refers to the resistance moment due
to the band of reinforcement m 1 taken on its own; that is, neglecting any
interaction effect of the other band. Similarly, m 2 refers to that of the
reinforcement band labelled m 2 taken on its own. In accordance with our
convention, a moment axis shown as a full line indicates positive flexural
strength (i.e. reinforcement near bottom face of slab); a moment axis
shown as a broken line indicates negative flexural strength (i.e. reinforcement
near top face of slab).
Figure 8.3-2 shows part of a yield line in a slab in which the
reinforcement bar spacing is s, measured in the direction of the moment
axis. The quantity As[y is the yield force in the reinforcement bar, having
components of As/y cos 4J 1 and As/y sin 4J 1 respectively in the directions
normal and tangential to the yield line, where 4J 1 is the angle between
the yield line and the moment axis. The label m 1 on the moment axis shows
that the slab has a yield moment of m 1 per unit width, i.e.
m1s = As[yz
where z is the lever arm.
If we let mn denote the normal yield moment (or the normal moment as
it is usually called) per unit length of slab along the yield line, and let mns
denote the twisting moment per unit length of slab along the yield line,
then
Moment
axis
Fig. 8.3-2